The etymology for the constant π comes from the fact that it's the first letter of the words periphereia (periphery), and perimetros, (perimeter). But it's also the first letter in peripateia, which defines this show and always has; periphrasis, which defines Rose, and Ten as well, and only means anything when you apply it to love; perishable, which ditto Rose and Ten, but only by half; periscope, which is how he sees the world, and perinatal, which is what he still is; periodicity and the Siege Perilous, which is what the season's about; perineum, the no-place between the worlds of divinity and excretion, inspiration and burning off what's not needed, breathing in and breathing out; perigon, or an angle equal to 360 degrees, coming back home; periapt, Ten being the charm she wears against danger even though she never needed it; perikardios, around the heart we're circling; perigee and perihelion and perilune, the closest you can be to the Earth, to the sun and the moon, without touching them, without falling in; and peri, a word with which we're familiar: the angel that has fallen, the fairy that takes you away. (And the person who played this game with the Doctor in the Big Finish serial "...Ish," a.k.a. the Who story written precisely for Jacob.)
Also known as Archimedes's constant and Ludolph's number, π is the ratio of a circle's circumference to its diameter, in Euclidean geometry, or the ratio of a circle's area to the area of a square whose side is the radius. π is irrational, meaning it can't be written as the ratio of two integers, and transcendental, meaning there's no polynomial with rational coefficients of which π is a root. The latter means that π is not constructible: because the coordinates of all points that can be constructed with a compass are constructible numbers, it is impossible to square the circle: it is impossible to construct with a compass a square whose area is equal to the area of a given circle. But the best definition I've ever seen is this: a circle with a diameter of one has a circumference of π. Meaning that it takes exactly π rotations to end up where you started, working your way around the wheel. Irrational and transcendent, but there you have it: what should be easy, matching a static square -- four hearts, two sets of twins -- to a circular journey is impossible, and yet you end up where you started nonetheless, and there's never been a circle that wasn't stronger than this fact, thanks to π. But what you can't construct can still be deconstructed, even if it takes thirteen episodes: On the other side of Hell, we burn off what doesn't work, and that amounts to 4 minus π: just a smidge less than one whole heart.